Abstract Image set classification using manifolds is becoming increasingly more attractive since it considers non-Euclidean geometry. However, with the success of dictionary learning for image set classification using manifolds, how to learn an over-complete dictionary is still challenging. This paper proposes a novel prototype subspace learning method, in which a set of images is represented by a linear subspace and then mapped onto a Grassmann manifold. With this subspace representation, class prototypes and intra-class differences can be represented as principal components and variation subspaces, respectively. Isometric mapping further maps the manifolds into the symmetrical space via collaborative representation, which permits a closed-term solution. The proposed method is evaluated for face recognition, object recognition and action recognition. Extensive experimental results on the Honda, Extended YaleB, ETH-80 and Cambridge-Gesture datasets verify the superiority of the proposed method over the state-of-the-art methods.

中文翻译：

---

使用 Grassmann 流形进行图像集分类的原型学习和协作表示

摘要 由于考虑了非欧几何，使用流形的图像集分类变得越来越有吸引力。然而，随着使用流形进行图像集分类的字典学习的成功，如何学习一个过完备字典仍然具有挑战性。本文提出了一种新颖的原型子空间学习方法，其中一组图像由线性子空间表示，然后映射到 Grassmann 流形上。通过这种子空间表示，类原型和类内差异可以分别表示为主成分和变异子空间。等距映射通过协作表示将流形进一步映射到对称空间，这允许封闭式解决方案。所提出的方法被评估用于人脸识别，物体识别和动作识别。在 Honda、Extended YaleB、ETH-80 和 Cambridge-Gesture 数据集上的大量实验结果验证了所提出的方法优于最先进方法的优越性。